Inequality($x\geq QM \geq AM \geq GM \geq HM \geq y$)
Basel's Problem
$$1+\frac{1}{4}+\frac{1}{9}+\cdots = \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi ^2}{6}$$
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Sum of odd numbers
Proof of $$1+3+5+\cdots = n^{2}$$ Count the number of balls in the L shaped regions.Notice that they are odd numbers. Furthermore,count the number of balls considering the length or the breadth(they will turn out to be the same). Sum of all balls = (number of balls on the length)$^{2}$.
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